Rdifferent balls b 1 , . . , b r are to be randomly put into n different urns u 1 , . . , u n (r ≤ n). what is the probability of the following events? (a) urns u 1 , . . , u r each contains exactly one ball; (b) no urn contains more than one ball; (c) urn u 1 contains exactly m balls (m ≤ r).

Aspacecraft can attain a stable orbit 300 kilometers above earth if it reaches a velocity of 7.7 kilometers per second. the formula for a rocket's maximum velocity v in kilometers per second is vequalsminus0.0098tplusc ln upper r, where t is the firing time in seconds, c is the velocity of the exhaust in kilometers per second, and r is the ratio of the mass of the rocket filled with fuel to the mass of the rocket without fuel. find the velocity of a spacecraft whose booster rocket has a mass ratio of 20, an exhaust velocity of 2.1 km/s, and a firing time of 15 s. can the spacecraft achieve a stable orbit 300 km above earth?